The solubility product of aluminium sulphate is given by the expression

Options

A. `4s^(3)`
B. `6912s^(7)`
C. `s^(2)`
D. `108s^(3)`

Answer

To find the solubility product (Ksp) of aluminium sulphate (Al₂(SO₄)₃), we can follow these steps:

### Step 1: Write the Dissociation Equation
Aluminium sulphate dissociates in water according to the following equation:

\[ \text{Al}_2(\text{SO}_4)_3 (s) \rightleftharpoons 2 \text{Al}^{3+} (aq) + 3 \text{SO}_4^{2-} (aq) \]

### Step 2: Define Initial Concentrations
Assume the initial concentration of aluminium sulphate is 1 M. At the start (before dissociation), we have:

- [Al³⁺] = 0 M
- [SO₄²⁻] = 0 M

### Step 3: Define Change in Concentrations
Let the solubility of aluminium sulphate be \( s \). As it dissociates, the changes in concentration will be:

- [Al³⁺] will increase by \( 2s \) (since 2 moles of Al³⁺ are produced for every mole of Al₂(SO₄)₃)
- [SO₄²⁻] will increase by \( 3s \) (since 3 moles of SO₄²⁻ are produced for every mole of Al₂(SO₄)₃)

At equilibrium, the concentrations will be:

- [Al³⁺] = \( 2s \)
- [SO₄²⁻] = \( 3s \)

### Step 4: Write the Expression for Ksp
The solubility product (Ksp) is given by the expression:

\[ K_{sp} = [\text{Al}^{3+}]^2 \cdot [\text{SO}_4^{2-}]^3 \]

Substituting the equilibrium concentrations into the Ksp expression:

\[ K_{sp} = (2s)^2 \cdot (3s)^3 \]

### Step 5: Simplify the Expression
Now, simplify the expression:

\[ K_{sp} = (2^2 \cdot s^2) \cdot (3^3 \cdot s^3) \]
\[ K_{sp} = 4s^2 \cdot 27s^3 \]
\[ K_{sp} = 108s^5 \]

### Final Result
Thus, the solubility product of aluminium sulphate is:

\[ K_{sp} = 108s^5 \]